To find the equation in slope-intercept form \( y = mx + b \) from the given table, we start by identifying the slope \( m \) and the y-intercept \( b \).
First, let's observe the values of \( x \) and \( y \) from the table:
\[ \begin{aligned} (0, 0) \ (2, 2) \ (5, 5) \ (-3, -3) \ (10, 10) \ (-8, -8) \ (15, 15) \ (-13, -13) \end{aligned} \]
From these observations, we can deduce that the relationship between \( x \) and \( y \) seems to always result in \( y = x \). Now, we can calculate the slope \( m \) using two points, for instance, \( (0, 0) \) and \( (2, 2) \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{2 - 0} = \frac{2}{2} = 1 \]
Next, since the point \( (0, 0) \) is on the line, it tells us that the y-intercept \( b \) is \( 0 \).
Thus, the equation in slope-intercept form is:
\[ y = 1x + 0 \]
This simplifies to:
\[ y = x \]
Therefore, putting it in the format requested, the final equation is:
\[ y = x + 0 \]